#
# Demonstrates the usage of hierarchical partial pooling
# See http://mc-stan.org/documentation/case-studies/pool-binary-trials.html for more details
#

import pymc3 as pm
import numpy as np

def build_model():
    data = np.loadtxt(pm.get_data('efron-morris-75-data.tsv'), delimiter="\t", 
                      skiprows=1, usecols=(2,3))
    
    atbats = pm.floatX(data[:,0])
    hits = pm.floatX(data[:,1])
    
    N = len(hits)
    
    # we want to bound the kappa below
    BoundedKappa = pm.Bound(pm.Pareto, lower=1.0)
    
    with pm.Model() as model:
        phi = pm.Uniform('phi', lower=0.0, upper=1.0)
        kappa = BoundedKappa('kappa', alpha=1.0001, m=1.5)
        thetas = pm.Beta('thetas', alpha=phi*kappa, beta=(1.0-phi)*kappa, shape=N)
        ys = pm.Binomial('ys', n=atbats, p=thetas, observed=hits)
    return model

def run(n=2000):
    model = build_model()
    with model:
        trace = pm.sample(n, target_accept=0.99)

    pm.traceplot(trace)

if __name__ == '__main__':
    run()
